Tim Scarfe: belief

Transcript context

…Well, depending on who you ask, you'll get very opinionated answers, but generally, you know, I it's when I started learning category theory, I was like, well, I'm never gonna go to 2 categories. That seems complicated. Now I say I'm never gonna go higher than 2 categories because that seems too complicated, but people do 3 categories, infinity categories. And and you can really start building up these relationships higher and higher and get this really comprehensive theory that that becomes a very different beast in some ways. There is a school of thought that our brain works in this way. So we think using, like, the the the symbols and these categories and so on, And then there's and then there's the notion of the universe is a certain way, and we understand the universe with that kind of interface. So it's almost like the driver for this is, here's an interface. Here's how we think. Here's how the universe works. Let's program computers in that way. That's that's that's a that's a big question. It's it's what what happens with these things is that when we start adding more levels, right, more is different, and that's the thing we start seeing in higher categories. When we add different kinds of relationships and morphism, you start seeing these things that can be perhaps more most aptly described as emergent effects. Right? Because if you have 2 things and you want to study their behavior as a composite, well, you can either study their behavior individually and look at the joint behavior, or you can compose the systems and look at the behavior of the composite. And what we often found is these are not the same. In many compositional cases, these are isomorphic, but often there is a map going 1 way but not the other. So you have to track. You start to track since this isn't isn't an equality anymore, you have to start tracking this higher self. But now this itself might be a part of another system that gives rise to this plethora in levels and levels of emergent effects. So that's 1 of the problems with higher category theory is that it's just so hard for us for with our complexity of minds to do this. So it's certainly an open question of what is the best substrate, how to encode these things, and people have done a lot of work in in programming language theory of encoding not just data structures and and algorithms, but but, type theories that that these algorithms are hosted in in some categorical way.…

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